Triangle Calculator
Enter the three side lengths of a triangle to find every angle, its area, and its perimeter instantly.
Example
For a triangle with sides a = 3, b = 4, c = 5:
Angle A = acos((4²+5²-3²)/(2·4·5)) = 36.87°
Angle B = acos((3²+5²-4²)/(2·3·5)) = 53.13°
Angle C = acos((3²+4²-5²)/(2·3·4)) = 90.00°
s = (3+4+5)/2 = 6
Area = √(6·3·2·1) = 6
Perimeter = 12 → Right, scalene triangle
How it works
Enter sides a, b and c. The tool applies the law of cosines for each angle and Heron's formula for area, after validating the triangle inequality.
Good to know
This Triangle Calculator solves a triangle from its three side lengths (the SSS case): type in sides a, b, and c, and it returns all three interior angles, the area, the perimeter, and a classification of the triangle. It is built for students checking geometry homework, DIY and trades workers laying out angled cuts or bracing, and anyone who knows the lengths of three sides and needs the angles or area without doing the trigonometry by hand.
Reach for it whenever you can measure all three sides but cannot easily measure the angles — for example, verifying that a corner is square (look for a 90 degree angle), checking whether three boards will actually close into a triangle, or finding the floor area of a triangular space. The result updates live as you edit any field, so you can experiment with lengths and watch how the angles respond.
To read the output: each angle is labeled by the side it sits opposite, so Angle A faces side a, and the largest angle always faces the longest side. The "Type" line combines two facts — a side description (Equilateral, Isosceles, or Scalene) and an angle description (acute, right, or obtuse) — for example "Right, scalene." Values are rounded to three decimals, and the note line shows the angle total as a self-check; it should read 180 degrees.
One practical caveat: this tool only accepts three sides, not a mix of sides and angles, so it cannot solve SAS, ASA, or AAS setups directly. Also keep your units consistent — sides in the same unit yield a perimeter in that unit and an area in that unit squared — and if the calculator reports a triangle-inequality error, re-measure, because no triangle can exist when one side is as long as or longer than the other two combined.
Frequently asked questions
What is the triangle inequality and why does it matter?
For a valid triangle, every side must be shorter than the sum of the other two (a+b>c, a+c>b, b+c>a). If any side equals or exceeds that sum, no triangle exists, so the calculator reports an error instead of bogus angles.
Why do the three angles always add up to 180 degrees?
In Euclidean geometry the interior angles of any triangle sum to exactly 180 degrees. The tool shows the computed sum so you can confirm the result; tiny rounding (like 179.999) is just floating-point display.
Is my data uploaded anywhere?
No — this calculator runs entirely in your browser; nothing is uploaded.
Is it free?
Yes, completely free with no sign-up and no limits.
People also ask
How do you find the angles of a triangle if you only know the three sides?
Use the law of cosines for each angle: cos(A) = (b² + c² − a²) / (2bc), then take the inverse cosine. This calculator does that automatically for all three angles, giving the angle opposite each side you enter.
Can a triangle calculator tell if a triangle is a right triangle?
Yes. After computing the angles it checks whether the largest one is 90 degrees; if so it labels the triangle 'right.' You can also verify it yourself with the Pythagorean relationship a² + b² = c² for the longest side.
What is Heron's formula used for in this tool?
Heron's formula finds a triangle's area from its three side lengths alone, without needing the height. It computes the semi-perimeter s = (a+b+c)/2, then area = √(s(s−a)(s−b)(s−c)), which is exactly how this calculator returns the area.
What does it mean when a triangle is called scalene, isosceles, or equilateral?
Equilateral means all three sides are equal, isosceles means exactly two sides are equal, and scalene means all three sides differ. This calculator reports which category your sides fall into alongside the angle type.
Why can't any three numbers form a triangle?
Three lengths form a triangle only if each side is shorter than the sum of the other two; this is the triangle inequality. If one length is equal to or larger than the sum of the other two, the sides cannot meet to enclose an area, so no triangle exists.
What units does the triangle calculator use for area and perimeter?
It is unit-agnostic: it works in whatever unit you enter the sides in, as long as all three match. The perimeter comes out in that same unit and the area in that unit squared (for example, centimeters give a perimeter in cm and an area in cm²).
Can this calculator solve a triangle from two sides and an angle?
No, it only handles the three-sides (SSS) case. Setups that include angles, such as two sides and an included angle (SAS) or two angles and a side (ASA/AAS), would need a different method or tool.
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